Momentum conservation homework

[scryedzxp]

Say there are two objects, A and B. A is moving with X velocity and B is at rest. Upon collision, what factor determines whether A will rebound off of B and B will stay at rest. Also, what determines if the two objects will "stick" together or move in the same direction as A? I believe it has mostly to do with B's mass, but I've tried using the law of momentum conservation and that didn't work out too well (but I might've been doing it wrong).

 

[DM]

I'm pretty confident you can find this in almost any physics textbook. I see two answers to your problem in which are more or less dependent of each other. State your initial ideas to this problem.

 

[StatusX]

B will never stay at rest, unless there is some other force on it. If you were talking about A stopping, this will happen if the collision is elastic, dead on (so that B doesn't go off at an angle), and if the two objects have the same mass. Then A will stop and B will continue with the velocity of A.

An elastic collision is one where kinetic energy is conserved, and an inelastic is one where it isn't. Which occurs depends on factors like the materials of the objects (eg, billiard balls are more likely to collide elastically, while lumps of clay will probably collide inelastically). The objects sticking together would be an inelastic collision, as some of the kinetic energy would be converted into internal energy (ie, heat and the structural change of the objects that results from the collision, along with the energy binding the two objects).

 

[DM]

B will never stay at rest

Not true. B can always be a wall, hence why object A would rebounce.

 

[StatusX]

Then, depending on how you think of things, there is an opposing force on B (the nails, ground, whatever), or the entire Earth recoils. Nothing stays at rest when a net force is put on it.

 

[krab]

StatusX is correct. For B not to move, its mass would have to be infinite. Momentum is conserved, so if B is a wall, and the collision is elastic, the Earth receives momentum change 2mv. If inelastic, the momentum change is mv.

Sorry Status, simultaneous response.

 

[DM]

Object B would move atomically.

A is an elastic ball and B is a brick wall. You never see the wall moving.

Atoms forming the wall structure would move, but never visually to us, humans.

 

[mybsaccownt]

without actually researching this first...(using an observation instead)

i believe it has to do with the time that the objects are colliding and the material they are made of

for example, in billiards...

you can either have the balls collide and both go somewhere, or if you hit it hard enough, the ball that was initially moving will stop moving where the collision takes place and the other ball will move very fast

that cancels mass out as the factor

also, in order to get the moving ball to stop at the place where it collided with the ball at rest, it has to be moving very fast, so when the collision takes place, it's a very very brief collision

if the ball is moving slowly, it might roll along with the ball it collided with or bounce off a bit

ok, so velocity has something to do with it

but imagine if the ball that was at rest was made of dough...

so it definitely has to do with the materialit really makes sense to me, from my observations of billiards, that velocity (or time spent colliding) and material are what determine the kind of collision

 

[DM]

i believe it has to do with the time that the objects are colliding

Whether they are in contact for a measurable time or just for a split second, each object is in contact with each other for the same time. They therefore obey Newton's third law in which states that the objects exert an equal but opposite force on each other.

so it definitely has to do with the material

This is undoubtedly true. There are objects that coalesce and others that bounce.

 

[mybsaccownt]

"There are two different types of collisions: elastic and inelastic. To understand the difference between them, it is necessary to consider a two-body impact as a deformation process, where the kinetic energy of the bodies transforms into other forms of energy - generally, deformation, heat and sound. According to material elasticity science, the potential energy of deformation can be transformed wholly or partially back to a kinetic one. The remanining energy of deformation, as well as the energy conversion into heat and sound can be regarded as a loss of kinetic energy. Loss-free collisions, where the energy losess during the colliding process are small such that the total kinetic energy reamins almost invariable, are callest elastic. Inelastic collisions occur when the losses of kinetic energy are not negligible. It is important to remember that in an isolated system, the total energy incorporating all energy types is constant."

"There is a measure of the elasticity of the collision, called the coefficient of restitution, e:

e = (V'2 - V'1)/(V1 - V2)that depends only on the elastic properties of the colliding objects. The coefficient of restitution is the ratio of the differences in velocities before and after the collision, divided by the difference in their velocities before the collision. A perfectly elastic collision has a coefficient of restitution of 1. A perfectly plastic, or inelastic collision has e= 0."

The coefficient of restitution tells us what kind of collision it is and it is only dependent on velocities of both objects before and after the collision.

"If the mass of the second object (that is at rest before the collision) is much greater than the mass of the first one m2>>m1, in the case when v2 = 0. The change in kinetic energy is equal to the initial kinetic energy.

that is almost all mechanical energy can be converted into internal energy."

hmm

so I guess this had already been answered in the first paragraphsimple answer...

the change in kinetic energy tells you which type of collision

how do you know how much the kinetic energy is going to change, well two lumps of clay, all (most of) the kinetic energy will go into deforming the objects, two diamonds will just bounce off of each other (almost no deformation), kinetic energy will be conserved

so, material, and mass determine the type of collision that will take place

(i'd like to say velocity, but i don't think the quoted material really implies that, since the velocities after collision depend on material and mass...)

the information in quotes is from my physics class earlier this year

 

[DM]

the change in kinetic energy tells you which type of collision

And by "which type of collision", you surely referring to how fast the collision occurs, right?

In scientific terms, "type of collision" implies elastic or inelastic collisions.

(i'd like to say velocity, but i don't think the quoted material really implies that, since the velocities after collision depend on material and mass...)

Kinetic energy is the velocity at which the objects move. The linear conservation of momentum states that change in momentum before and after impact of two elastic objects are the same, hence 0.

You say that the velocities after collision depend on the material and mass of the object. What about the approaching collision speed? Why should it be any different?

A lighter object is more able to travel faster than a heavier object, hence why the approaching speeds CAN be different.

 

[mybsaccownt]

And by "which type of collision", you surely referring to how fast the collision occurs, right?

In scientific terms, "type of collision" implies elastic or inelastic collisions.

i mean type as in...elastic or inelastic

Kinetic energy is the velocity at which the objects move. The linear conservation of momentum states that change in momentum before and after impact of two elastic objects are the same, hence 0.

You say that the velocities after collision depend on the material and mass of the object. What about the approaching collision speed? Why should it be any different?

throw a diamond at another diamond...the initial velocity doesn't matter, it'll be elastic

throw a lump of dough at a wall, it'll be mostly inelastic regardless of the initial speed

the reason i want to say velocity is because if you threw a diamond at a block of wood at a low velocity it would bounce off, if you threw it fast enough it would get stuck in the wood...but the reason it changes is basically because of the material,

you couldn't throw a piece of dough at another piece of dough with any velocity such that they would have a mostly elastic collision,

you couldn't throw a rubber ball at a wall fast enough for the rubber ball to stick to the wall,

even in extreme cases of velocity, the outcome doesn't change for the examples i listed above

this is not true for mass

could you make a block of wood so massive that no matter which speed you throw a rubber ball at it, it would be an elastic collision? yes

could you make a block of wood so light that the rubber ball would have a partially inelastic collision? yes

could you choose a hard material such that the collision would always be elastic when you throw a rubber ball at it, at any speed? yes

could you choose a material soft enough to have an inelastic collision with a rubber ball, at any speed? yesso you can choose extreme cases of velocity where the outcome only depends on the materials or mass

this would imply that velocity is not what determines what kind of collision will occur, but it can in some cases

that's why i want to say velocity but i think material and mass are more important

A lighter object is more able to travel faster than a heavier object,

any object of any mass can travel at any speed provided sufficient force

hence why the approaching speeds CAN be different.

uh...yeah, velocity isn't a constant...what's your point?

 

[DM]

throw a diamond at another diamond...the initial velocity doesn't matter, it'll be elastic

Yes, I'm aware of that. However elastic the objects are, the velocities will always differ when traveling at different readings. So whilst the initial velocity, as you very well deduce, does not have any impact on the type of collision, it'll always have an affect on the speed after collision and before collision. Hence why Isaac Newton formulated the coefficient of restitution law:

V=eu (this only applies to elastic objects!)

throw a lump of dough at a wall, it'll be mostly inelastic regardless of the initial speed

I do not disagree with this point, never did. If I gave the impression, I do apologise.

any object of any mass can travel at any speed provided sufficient force

Yes, indeed. You missed the point however. You're thinking of two objects traveling at the same speed. In most real life cases, two objects, one that is much ligther than the other will have different collision effects.
Let's assume a car collides directly against a truck. The car travels twice the speed of the truck as it's lighter and therefore accelerates at a much faster rate. What will happen at impact? In which direction do you think will the two objects move after the collision?

uh...yeah, velocity isn't a constant...what's your point?

The point is of course that whilst objects do collide at the same speed, there are other cases such as the one pointed out above.

By the way, when I state "whilst the initial velocity does not have any impact on the type of collision", written in the first paragraph, this is not entirely true. I stated such thing just to push aside the speed variable for a while and concentrate solely on the collision. In reality, speed does have an impact on the type of collision but ONLY in the most complex and perhaps extreme cases. An example of such complex cases is for instance a water pipe streaming water against a brick wall where the water coalesces or adheres to the wall. If I was to spout the water with great velocity, the water pipe, in which by the way is very near to the wall, would release water particles that in the majority would bounce off the wall.

I would like to reiterate that this is only in cases of great complexity and the above example may not be a paradigm of such cases.

 

[mybsaccownt]

i see what you mean

but the velocities before and after the collision can be used to determine the type of collision

it doesn't matter what the velocities are, you're taking a ratio of the difference in velocity before compared to after collision

what i meant was, although you can use this information to determine the type of collision...the velocities after the collision depend on material and mass

so it seems velocity is always dependent on mass and material and that's why i don't feel right stating that velocity itself is a big factor in the collisions